Page 107 - ICSE Math 6

Cardinality

Cardinality of a finite set is the number of elements in the set. Maths Info
Cardinality of an infinite set is not defined. The cardinality of Cardinality of an empty set is
a set say, X is denoted by n(X). For example, the cardinality of zero, i.e., n(f) = 0.
A = {–5, –9, 0, 2, 3} is 5, i.e., n(A) = 5.

EXERCISE 7.2

1. Identify the following sets as finite, infinite or empty sets.
(a) A = {x | x > 9, x ∈ N} (b) X = {x | x is an even prime number}
(c) B = {2, 4, 6, 8, 10, …} (d) C = {x | –4 < x < –2, x ∈ W}
(e) D = {x | x < 0, x ∈ W} (f) F = {x | x is a vowel in the word RHYTHMS}

2. Write the following sets in the tabular form and find their cardinality.
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(a) A = {x | x ∈ W and x < 26}
(b) Y = {x | x is a letter of the word CARDINAL}
(c) A = {x | 4x – 24 = 0, x ∈ N}
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(d) B = {x | x < 10, x ∈ Z}
3. Find n(X) for each of the following.
(a) X = {0}
(b) X = {x | x is a letter of the word INTERSECTION}
(c) X = {x | x is an even number and also divisible by 0}
(d) X = {x | x is a 3-digit number formed by 5, 6, 8 without repetition}

(e) X = {x | 9x + 36 = 0, x ∈ Z}
(f) X = {x | 4x ≥ 0, x ≤ 3, x ∈ W}
(g) X = {x | x is a prime number having 3 divisors}

AT A GLANCE

¾ A collection of well-defined objects is known as a set and every object forming a set is known
as a member or an element of the set.
¾ A set with finite number of elements is known as a finite set and a set with infinite number of
elements is known as an infinite set.
¾ A set which has no element is called an empty set or null set.
¾ The number of elements in a set is known as its cardinality.

MENTAL MATHS

1. Which of the following collections form a set?
(a) Odd whole numbers less than 120.
(b) Three most beautiful actresses of Bollywood.
(c) All the dull students of your class.

(d) All the numbers greater than 0.

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